Gary
Last year we left the pump on, we live in teh south of england so we don't get really harsh weather, but the pond does freeze over from time to time. We found that leaving it on created a bad problem with weed, it was a very fine green weed that covered the whole pond. In previous yeasr the pump has always been turned off and we didn't have the same prblem so this year its off! Hope this helps. I am no expert on ponds we inherited ours with the house ten years ago and we basically don't do much. We forget to feed the fish half the time but they seem to survive ok!
Good luck
Linny